Mr. Johnson, Wisconsin Republican, sued in January to take away his fellow lawmakers’ health care subsidies, saying members of Congress and staffers who must enter the Obamacare marketplace should not get financial perks that regular Americans cannot obtain.

In this case, those perks are the percentage of premiums that Congress has long covered for its employees, and which are continuing even though many of those employees were pushed off their government plans and into Obamacare’s exchanges.

“It was apparent by the briefs presented and the questions asked that the issues raised by this administration’s unlawful executive actions represent a serious threat to the delicate constitutional balance between America’s three coequal branches of government,” Mr. Johnson said Monday.

Obama administration lawyers, though, say Mr. Johnson can’t show any harm from having the government pay the premium subsidy, so he doesn’t have standing to sue.

The lawsuit is one of a number of challenges to President Obama’s health care law that are still making their way through the courts, following last week’s ruling striking down the administration’s mandate that for-profit companies’ insurance policies must cover the costs of their female employees’ contraceptives.

The health overhaul survived the main challenge to its existence in 2012, when the justices upheld its “individual mandate” under Congress’s taxing authority. But it wasn’t the final word on the law, and remaining challenges — if successful — could be fatal to Mr. Obama’s signature domestic achievement.

The lesser-known lawsuits challenge the legal and practical underpinnings of the Affordable Care Act, ranging from whether the bill was properly written in Congress to whether the administration can pay subsidies even to states that refused to set up their own exchanges.

These cases are pending before the U.S. Circuit Court of Appeals for the District of Columbia, and decisions could come at any time.

The D.C. panel also is mulling a challenge from Priests for Life, who are at the vanguard of the second wave of faith-based challenges to the contraception mandate. Religious nonprofits say they should not have to fill out a form that authorizes an insurer or third-party administrator to pay for contraceptives in their place — an approach the administration offered as an “accommodation” for faith-based hospitals, schools and charities.

Mr. Johnson’s case is being heard by Chief Judge William C. Griesbach of the Eastern District of Wisconsin. It’s not clear when he might rule on whether Mr. Johnson has standing to move the suit forward.

Mr. Johnson filed his suit against the Office of Personnel Management, the agency that last year said members of Congress and their staffs could keep subsidies that paid for up to 75 percent of their premiums — even though they must pick health care plans from the state-based marketplaces.

Even some Republicans have questioned his lawsuit.

Rep. F. James Sensenbrenner Jr., a fellow Wisconsinite Republican, called the lawsuit “an unfortunate political stunt.”

White House press secretary Josh Earnest highlighted intra-GOP divisions during his daily briefing on Monday and said the administration does not intend to cede ground on its signature law.

“Our efforts to enforce this law and to implement this law in a way that maximizes benefits for the American people and expands access to health care is something that we’re moving forward on,” he said.